Mr. Khan’s critics say that his model is really a return to rote learning under a high-tech facade, and that it would be far better to help children puzzle through a concept than drill it into their heads....

Today, the Khan Academy site offers 2,700 instructional videos and a constellation of practice exercises. Master one concept, move on to the next. Earn rewards for a streak of correct answers. For teachers, there is an analytics dashboard that shows both an aggregate picture of how the class is doing and a detailed map of each student’s math comprehension. In other words, a peephole.

Diane Tavenner, chief of the Summit chain of four charter schools, said that at first she was ambivalent about using Mr. Khan’s software. It would require buying laptops for every student and investing in more Internet capacity. And she found the Khan Academy model of instructor and blackboard — albeit a digital one — to be a bit too traditional.

Rote learning. Teacher and blackboard. Traditional. You'd think the teacher herself would be perfect at doing what this website does.

In the past, math class at the Summit schools was always hands-on: the class worked on a problem, usually in small groups, sometimes for days at a time. But getting an entire class of ninth graders to master the fundamentals of math was never easy. Without those, the higher-level conceptual exercises were impossible.

That is where the machine came in handy. The Khan software offered students a new, engaging way to learn the basics.

So.... let the website do the traditional work of teaching the fundamentals so the teacher can spend more of her time subjecting the kids to group projects?

ADDED: Pollcode isn't working right now. The options should be:

How do you feel about group projects in school?

1. Loathe them. What this article does is point the way to home-schooling.

2. They're part of a nice mix. It's good to free the teacher to spend more time on what she loves.

3. Love 'em. Let the computer do the technical stuff and bring on the group projects!

I'll turn it into a poll if I can get the site to process the code.

IN THE COMMENTS: TMink says:

The Kahn Academy stuff is killer. I use it with my kids and recommend it at work every week. There is nothing about the Kahn approach that necessitates group work in my understanding.

The thing that teachers HATE about the Kahn approach is that it is detail rich and gives tons of info regarding how well each student is doing at the touch of a button. It requires the teachers to teach because it takes away excuses through data.

154 comments:

It seems like everything my kids do in school is based upon group projects. It is alwayws the same, one or two kids in the group do the work, and everyone else coasts along -- so I guess group projects are not so much about mastering material as preparing for real life.

I decided to take an online artificial intelligence class this semester (and it was free...awesome). As someone who hadn't done any form of advanced math in nearly a decade I watched some of the pre-reqs that the AI class linked to. They were Khan Academy classes. It may be rote memorization on a high tech blackboard, but he's very clear about what he's teaching and why and his examples, though walkthroughs were never easy ones, but ones that help you understand the concept and build a base to work from in the future. I know it's amazing that a simple, well-taught lecture might actually help people to learn, but it definitely helped me.

Just my own experience, but group projects in school seemed to follow a fairly ballistic trajectory. Early in my schooling, they were great, culminating in fun/effectiveness somewhere around junior high. It seems as students get older and more jaded and/or cynical of those around them, the group effort thing cratered spectacularly once I got to college.

I hated group projects when I was in school, and I hate them as much when my kids are subjected to them.

Here's the problem: in the real world, group projects are generally divided by both capability and responsibility. If one member's work sucks, the other members notice, and word on that problem tends (at least in well run organizations) to get around, and upstairs.

Group projects in schools tend to be divided only by grade. One kid does all the work; all the rest slide and get an A. No kid does any work; all slide and get Fs. Two kids do some B work and three do nothing; everyone gets a C.

I'm a college physics professor, and I'm really surpriseed by so many of these teachers who disdain the professor-at-a-blackboard way of teaching. Group projects can, in principle, help with some problem solving skills (especially necessary in math, physics, and chemistry), but it's an approach with an extremely low density of, well, actual content they can learn.

I spend most of my time at the blackboard, deriving equations. I tell my students not to bother memorizing many equations in physics. They should be able to derive what they need from first principles in most cases, even in the introductory course. There are no cheat-sheets in my exams. Completely closed-book for the intro courses (advanced courses I often do open-book and take-home, though).

And the students actually say they prefer my approach. Some of them have taken courses where the professor doesn't teach them material but has them work everything out in small groups, and the students seem to dislike this.

To make one more point, at least in physics: An entire year of introductory physics is spent covering material that was discovered over a hundred years ago. You will rarely get up to anything much more recent than the beginning of the 20th century (not until you take Modern Physics in your sophomore year) because so many of the laws of nature were discovered between the era of Newton and Einstein. That's two centuries plus of discovery, all of it heavily mathematically based.

So how could you expect to teach more than just a tiny subset of this through the method of group problem-solving? Are you expecting the students, given some simplified experimental results, to rediscover the laws of nature on their own? You can do that, but it takes a lot of time (it took the original discoverers 200 years!), and how can you fit 200 years' worth of material into two semesters this way?

Sometimes I wonder... do instructors assign group projects due to higher reasons (such as presenting the opportunity for a side lesson in developing social skills? Or something similar?)? Or do they do it because it cuts down on the work needed to grade such projects?

I full well believe that there are places for group assignments, but there were times in school to where I wondered if the specific project being given was one of them.

I agree with the trajectories suggested by Scott M and Tim. In grade school, group learning is ideal, because kids are still learning to socialize.

In High School, group learning is not optimal. My daughter was the one doing all the work. My son is the one waiting for someone else to finish. In College, group learning is a joke.

When I have taught face-to-face, I have preferred sitting in a circle discussing the topic with my students. That does make it difficult for students who have to learn how to extract what is important in my discussions (Here's a hint: If I mention it twice, it's important). My classes require the memorization of a certain amount of facts, and no amount of group learning can help with that. I will write on the board, but I am more comfortable walking through the classroom.

Now I only teach on-line classes. Those are definitely not for everyone, but I have students who really thrive in them.

Here's the problem: in the real world, group projects are generally divided by both capability and responsibility. If one member's work sucks, the other members notice, and word on that problem tends (at least in well run organizations) to get around, and upstairs.

This.

So how could you expect to teach more than just a tiny subset of this through the method of group problem-solving? Are you expecting the students, given some simplified experimental results, to rediscover the laws of nature on their own? You can do that, but it takes a lot of time (it took the original discoverers 200 years!), and how can you fit 200 years' worth of material into two semesters this way?

And this.

Schools say they do group projects because one can expect to do so many group projects in the adult world of work. But group projects in school and group projects at work are entirely different animals. At work it rarely happens that a bunch of undifferentiated workers are assigned a task to accomplish together with no specific responsibilities. In fact, I can't remember it ever happening.

I'll add my praise for the Khan Academy. Although I haven't looked at it myself, I have a student who was really struggling in my intro physics class this sememster. Smart kid, chemistry major, and capable in math. But he had problem solving skills. He went to the Khan Academy site and started working through their physics lessons on his own, and I immediately noticed his improvement in my class. It takes a more motivated student to do well with online material, but he's an example of this.

Also, we do, of course, have group projects in physics. That's how you do laboratory experiments. I make sure the groups are small, so you don't get too many free riders. There's a role for group activity, but I don't think it can replace the need for seeing a clear derivation up at the chalkboard, so that they can follow the flow of logic from the basic principles down to a conclusion.

The working world is full of group projects. Whether a large corporation, small business, or sole proprietorship, you can't expect to succeed without being able to work with, and, sadly for the independent-oriented, rely upon others.

That said, all of my success as part of a group dynamic I attribute to sports, none of it to school projects. There's a reason why so many sports metaphors are used to describe them.

In the old country, we did memorize the multiplication tables in grade school. It was not that hard; you could not escape them as they - or the standard traffic road signs - were printed on the inside covers of our exercize booklets.

In high school the standard system was that the teacher (Herr Lektor that is) would spend the first ten minutes of classtime calling on students to see if they had read and understood that day's homework assignment, and then spend the remaining 40 minutes of classtime teaching things not covered in the textbook.

The Kahn Academy stuff is killer. I use it with my kids and recommend it at work every week. There is nothing about the Kahn approach that necessitates group work in my understanding.

The thing that teachers HATE about the Kahn approach is that it is detail rich and gives tons of info regarding how well each student is doing at the touch of a button. It requires the teachers to teach because it takes away excuses through data.

As for group projects, I can remember occasionally some of us would get together informally and work on math or physics assignments helped along with a couple of pilsners, and also discussing more serious matters, such as girls, etc., but as far as the school was concerned this was a big no-no - the beer too.

A bunch of school districts in my area are using a site called IXL for math practice. Seems effective, at least as a change up. I watched my son work through a set of problems and was impressed at how much scrap paper he used. From what I've seen of son and daughter, they enjoy being able to solve a bunch of problems in succession. Rote works.

Frankly, if I had the time, I'd probably work through Kahn's stuff myself. I'd love to rote learn me some advanced physics and math.

Of course, what Kahn is offering is really nothing new. People used to learn on their own using things called "books."

In the course of my law reading I constantly came upon the word "demonstrate". I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof?

...

At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies.

When I took up fishing, I spent a lot of time practicing knots. I had some printed instructions and a spool of mono in my backpack and I would tie knots on the bus to work.

I wanted to be able to tie all the basic knots, quickly, without reference, in the dark.

Rote learning. It's useful.

On the other hand, I've spent almost no time learning computer programming by rote. Every reference I need is at my fingertips. One of the stupidest exercises in my life was my freshman Pascal class in which the teacher deducted for syntax errors on written examinations. That pushed me out of programming for about 15 years.

The group work fetish was taking hold when I did my ed classes in college. Also taking hold was the concept of letting students "discover" what they were supposed to learn. The theory is that if discovered, then it's better imprinted in the brain. It truly is a higher level of learning, which is why its horrible for children who are still developing and don't have any basics.

The basics and initial concepts need to be drilled and drilled. Eventually, the natural order of those concepts will unlock and then, and only then, will the student be capable of "discovery" of new concepts. Otherwise, it's like jumping into the deep end of the pool without knowing how to swim.

The effects of this on education were muted because the teachers did learn through drill and other traditional methods. However, any teacher under 35 has been taught under all this new theory and don't have the basics mastered themselves.

One of the stupidest exercises in my life was my freshman Pascal class in which the teacher deducted for syntax errors on written examinations. That pushed me out of programming for about 15 years.

I recall that as well (although it was PL/C, not Pascal).

In the prof's defense, however, there was very limited CPU time (you got a set number of job cards at the start of class and once they were gone, you were done), so being able to punch cards with no syntax errors was important.

Nowadays you just let the compiler catch the error and fix on the fly.

I did many group projects in Business School, which do somewhat prepare you for the dynamics of working, but what is the point in elementary? I had very few group projects in high school and almost none in elementary school.

And none ever in math! What on earth would be the point? Unless you are going to allow a group test, you are just ensuring that some people get no practice.

I'm glad the nuns made us memorize the times tables. I have that information at my fingertips still. You can use a calculator, but if you aren't able to mentally check it, you're liable to end up with garbage.

I have been astonished by how much my kids have been required to draw in high school. Cartoons and posters are de rigeur in virtually every subject, to the exclusion of writing. When I asked one of their teachers about this, i was told they were required to teach in this way.

No. 1, hands down. Just about the time a former student needs to use the knowlege that should be acquired in school, she'll be alone without a group to query, and without socially dominant members to concur with.

The group projects counter feint by the teachers is a way to avoid the work involved in figuring out who needs individualized help comprehending the material presented in the courseware. As Pogo neatly summarizes, reliance on group projects masks the deficits in learning/effort of the individual members of the group. I thought the whole idea of the Khan approach was to free the teacher from the day to day grind of teaching the basics so that they had the time to invest in individual students or small groups who needed further enlightenment. Perhaps this semi-custom approach doesn't fit well with the production line teaching philosophy. Smart kids also benefit by being able to jump ahead. My kids are older, but in the day, we were told that as long as they worked to grade level, that was all that was required of the teachers. Six years of private schools for each ensued, to their benefit.

model is really a return to rote learning under a high-tech facade, and that it would be far better to help children puzzle through a concept than drill it into their heads...

ROTE LEARNING is the foundation upon which you build other skills. Just like any skill you must practice the fundamentals...over and over and over until you have the skill down pat.

As in learning a musical instrument, like the guitar, you don't just pick it up and begin playing like Gary More or Eric Clapton. Even they practiced until their fingertips bleed.

GROUP PROJECTS: are bullshit. All they do is allow the kids who don't contribute or won't or can't contribute to free ride on the skills and hard work of those kids who do and who are motivated.

My daughter knew that in order to get to a good college it would require some very good grades and extra curricular activities to qualify for scholarships. Group projects were HELL on EARTH because she worked her butt off and basically did the entire project so she could get an "A" and keep up her GPA. The other lazy snots did nothing.

I think learning has always been a combination of rote and discovery. I looked at a few of the Khan lessons in Algebra and found them to be the careful step by step instructions a good teacher makes, but I suspect because it is presented on a computer the students may pay closer attention, and they can repeat what they do not understand. In today's complex technically rich work environment cross discipline group work is becoming the norm. For example Biomedical majors in our COE often work in group projects designing solutions for actual clients, and anyone working in a research lab quickly understands what a group effort means. One problem with group work, assuming it is a meaningful project, is that often teachers do not know how to teach a group to work effectively and to self monitor the participation of all members to ensure equal contributions.

This is very true. You can tell the professor that one person basically did nothing and try to sabotage their grade (which my friend and I tried to do once with a member who we were unable to reach and thus contributed nothing), but I don't think his grade actually got reduced. Sadly, this is sometimes true at work too, but it may show up in a performance rating.

we do, of course, have group projects in physics. That's how you do laboratory experiments.

Small groups in the science fields are valuable.

I took 6 years of science courses in high school instead of the bare minimum requirements of 3. Some of my electives were science...I know, NERD.

My lab partner all the way through high school (Belinda Chew....hi if you are out there) and I cooperated on all of the projects...biology, anatomy projects, chemistry. You couldn't have done the involved projects alone. We worked very well together.

Other put together lab partner groups didn't work out so well, again because of the difference in work ethic.

I guess I've been on Gulligan's island too long, but I just discovered Khan last week.

I've been learning math concepts that I never quite mastered in school. I'm really learning them this time and it's very fast. One great thing about his videos is that he dives right into it. No wasted time with intros - the first word out of his mouth starts the learning. If you did a time study of classroom instruction, I think you would find a lot of wasted time.

I'm not an education professional. I just want to learn fast, and I just can't find anything wrong with his stuff. Imagine the education you would get if you spent every day watching and doing along with that program. In a week, you can learn a whole semester of algebra.

I would love to hire a person who did that, and I would enthusiastically accept it if they had a degree from Kahn.

Oh, how I loathe group projects. They don't help anyone learn anything - and I was always the one who ended up doing all the work while the loser stoners I was teamed with "earned" MY grade. And this was 40 years ago, fer cryin out loud.

Someone asked about group projects in math - this is a more recent development. Rote learning is always bad, hands-on is always good, so you have to let the kids count blocks, say. In a major group project. Again, such nonsense. No one learns the math and we wonder why we lag in academic performance worldwide.

In high school, the only good group projects were the ones in classes like advanced history or advanced literature - subjects that were a bit more subjective and classes filled with like-minded kids who actually wanted to be there.

I really don't see how that would work for math or physics, though.

I recently saw a TV program on the Khan method being used in a charter school - the teacher loved it - she said that it took care of all the rote stuff that usually bored her, while she had way more time to spend with the kids who were having trouble or just needed a little more help. Clearly she was too smart for the public system.

About group projects, I always had a good semester long group project for my classes, UG and grad and majority of the students liked it a lot. I emphasized how it was useful later in work life to develop interpersonal skills and getting along in a group. There were usually one or two problem groups but addressing their complaints and mediating early on was key.

TosaGuy,The basics and initial concepts need to be drilled and drilled. Eventually, the natural order of those concepts will unlock and then, and only then, will the student be capable of "discovery" of new concepts.

To become a flight instructor I was required to learn (by rote) the "levels of learning":

RoteUnderstandingApplicationCorrelation

Understanding, Application and Correlation all depend on the Rote learning happening first.

You can tell the professor that one person basically did nothing and try to sabotage their grade (which my friend and I tried to do once with a member who we were unable to reach and thus contributed nothing), but I don't think his grade actually got reduced.

Or you could end up in a group with three guys who are best friends. Then when one of them flirts with you and you don't respond, they decide not to contact you and to ignore your requests for meeting times, telling your physics teacher at the end that you wouldn't help with the project.

My own personal experience with group projects has not been all that good. At UVA, my first semester as a new international student -- the professor asked us to form groups and I went around the class asking if I could be in their group. Nobody said yes -- they just looked at each other. I was reduced to tears at the end of the go around and I dropped the class. I told this to my adviser who was a very nice guy, and he must have relayed it to the prof. Because the next time the class was offered, the professor formed groups and he matched me well with a few nice people and I still keep in touch with one of them after all these years.

Kahn is a very good natural teacher. He reminds me of all the best teachers I've had.

That's the thing. Every student who used Kahn gets a great teacher. Due to technology, one great teacher can teach millions. This is of course a great threat to teachers. One time good people made buggy whips.

We will still need teachers, but maybe now they can be successful with more students. It's hard to argue we don't need something, and everything except "traditional" has been tried.

My children did not like most (middle/high school) group projects. It's not just that some people in the group do not do their share of the work, it's that they are disruptive and try to keep others in the group from working.

One group project they did like were building race cars from some wood and wheels. The teams then raced each other in their cars. This project let the students use different skills - building, painting, driving the race car (being small and flexible enough to get in and scrunch down helps), or being big, strong, and fast enough to push it at the start of the race. Everyone could contribute in some way, and not in a manufactured credit-for-just-showing-up way.

My kids' high school teaches math in groups and it is a horrible way to learn math. Everybody doesn't win. The kids who are really good at math don't contribute much to the group. The kids that needs to learn the math, don't learn it as well as they should because their peers aren't always good teachers. Unlike other subjects, only the kids who are already good at math can coast in math.

Left unsaid here is that Khan approach, with rote learning and instant objective feedback, is inimical to the current public school mindset, which is process oriented, not results oriented. Even in, especially in, math and science. The goal is foster "mathematical thinking"; whether the student can actually recount the times table is irrelevant. Then, when the student is below-grade level in math, he or she will qualify for remedial help with paraprofessionals. Possibly, he or she will be placed on an individualized education plan, and then qualify for additional, federal and state funded services. And students on IEPs won't count against a school's test scores. So, don't bother with the fundamentals, because some will struggle and hurt the overall numbers.

When I was hiring engineers, I was shocked at how many could not do things on their own. They skated in groups and relied on group grades. They could not think, create, or perform except as cheerleader in a group.

Ann,It (i.e. the Kahn Academy approach) is useful for an individual preparing for a major mathematical challenge like the CFA exams.I endorse the use of this system for people who have not been using college-level mathematics on a daily basis.

I didn't enjoy most group projects in school because I ended up doing most of the work and had no real power or control over the kids who didn't pull their weight or screwed it up for the rest of us (tattling was pretty much verboten in my day). There were outstanding exceptions, of course, but they were few and far between--and for the most part, the exceptions involved having selected the group members as opposed to having them "assigned." How unsurprising!

Wait, I can recall one group project in math class. However, it wasn't sanctioned by the teacher. It was a group of us bored with the days lesson collaborating to program our TI-81s so we could play blackjack.

IMHO, when a teacher gives a group project, they are either trying to skate for while, or they are trying to "share the wealth" - transfer the knowledge wealth of the smart kids to the dumber ones. It doesn't work in this environment any better than in the economic one. The result is the same, the haves produce enough for both, and if overtaxed and under-appreciated, refuse to do their best. Eventually all members end off worse, as both the haves and the have-nots are incentivized to give less effort.

Ask all to do their best and accept the unequal result. Stop trying to overpower nature - ride its wave.

Well, I work with college students, so consider what I do suitably modified.

Group work is good if used judiciously. You do not want to balance the groups. Otherwise the slower ones free-ride. Struggling with the material is part of mastering it.

Drill is exactly what today's students need. Of course everyone has to master concepts, but you can't reinvent the wheel every time you need to do some algebra. And it's not like high schools are doing a bang-up job of teaching concepts. Roughly half of the college sophomores and juniors I teach cannot divide by 1/2 or do other simple arithmetic, much less algebra.

Even worse, they cannot connect the sine or cosine of an angle with the sides of the given triangle. They need a calculator, and then they find the cosine of the inverse sine or whatever, and get it wrong. Which means a) they haven't had enough drill to get mastery and b) they don't understand the concept EITHER.

Or you could end up in a group with three guys who are best friends. Then when one of them flirts with you and you don't respond, they decide not to contact you and to ignore your requests for meeting times, telling your physics teacher at the end that you wouldn't help with the project.

Yeah, that sucks too. The guy who did nothing on the group project did finally try to in touch. He called and harrassed my roommates at 11 o clock the night before the project was due (when the other two of us were at the library working) then he called and bitched at me when I was telling him that the project was complete! At two in the morning! Jerk. That's why we tried to get his grade lowered. We didn't let him present, either.

College students will not, in general, ask for help from a professor. They are too afraid of looking stupid. The fact that I grade them and know exactly how smart they are doesn't matter for some reason.

(This is baffling to me personally because I was never embarrassed to ask when I don't know what's going on, I don't have that gene or something.)

If a student DOES ask a question, and they got something wrong, when you explain it to them, and they realize they said something wrong, they immediately start backpedaling from what they said.

I think the reason they do this is because they think every interaction with a professor is going to have some effect on their grade. That's all most of them care about. Understanding what is going on is secondary--all they want is to give you something that might satisfy you so they'll get points.

So one reason for group work is that students will ask each other.

Another reason for group work is that professors often times find it hard to know what misunderstanding a student has. We don't read minds. Supposedly chess masters don't "see" bad moves. Likewise, I don't "see" bad physics and it's an effort for me to follow someone who is doing it wrong. When students work with each other it is easier for them to see what other students are getting wrong. If you just worked through a misunderstanding you know exactly what it was and what someone needs to say to snap you out of it.

Group work is not a panacea. It does need to be used as one part of a strategy. I myself hated group work, until I was studying for prelims, with people who all worked hard and were on my level.

And that's another reason to sort the groups by ability. The smart ones may not want to or need to work together, and they won't have to carry the others. They can leave after five minutes. When the class thins out you can tutor the small groups.

2) They are used for communication only, with the purpose being to get all the information in one room to prevent having only half the picture when making decisions or getting an understanding of status. People will bullshit you much more if there is no one there with conflicting information. Just the presence of the other person prevents a lot of lies from getting started.

We use Kahn Academy in homeschooling as one among a number of tools. For some things, it's terrific; other times, it bores and irritates my kid. The key is in picking the right tool for the task--which, if you think about it, is a critical life skill, and thus an important thing--perhaps one of the most important things--to teach and model in its own right.

"The Khan software offered students a new, engaging way to learn the basics..."

What, beyond the basics, is taught in primary and secondary school? In math in particular, high school students won't get beyond basic integral calculus.

Math isn't an art, or a science; it's a discipline, which you learn by doing and by hard, lonely work. You would learn nothing from a brainstorming session with your classmates. Some hands-on experimentation would be great, but group projects are just a nonsense way for teachers to take some time off and put their feet up on the desk.

Homeschooling kids sounds like it would be a lot of fun. I raised two kids, and often when they wanted something valuable from me, I would make a test which required them to go research to find the answers or the method to the answers. After succeeding a number of times they started to ask for more. It's actually no more work than whining for stuff, and they developed the confidence that they could "win" and force me to give them what they wanted by knowing things, rather than whining longer. OWS kids needed similar training. Too late now.

Here is one that attempts to explain how gigundonormous the universe is.

At least 26 billion light years across. At least.

I've always considered estimates of how big the universe is or how much mass is in it to be akin to a dust mite trying to estimate the size of the Earth's oceans or the amount of water in it from behind a grain of sand buried two feet deep on a beach.

@Scott M:I've always considered estimates of how big the universe is or how much mass is in it to be akin to a dust mite trying to estimate the size of the Earth's oceans or the amount of water in it from behind a grain of sand buried two feet deep on a beach.

It sounds harder than it is. It may seem like no one could ever know that, but that simply isn't true.

How do we know the shapes of molecules? Well, we now have advanced microscopes and what not, but even in the 19th century they could tell. For example, by measuring the specific heat of a gas. That can tell you how many atoms are in a molecule and a lot about how they are arranged, and it is a very simple calculation based on very simple physics.

As for the size of the universe, the speed of light times the age of the earth gets you within a factor of 3 or so, and you can't get easier math than that. The age of the earth can be ballparked from radioactive decay rates, which are a trivial appplication of simple probability.

When I was an undergrad, I loathed group projects. I was continually amazed that supposedly intelligent professors thought there was anything valuable in letting 3-4 members of every group coast on whoever was foolish enough to start working on the project early.

As a grad student, I had a few experiences of group projects that weren't absolute disasters. Even then, I had one where 3 of the 4 group members went to the professor and stated flatly that #4 was dead-weight. I will say that educationally, giving weekly updates on a semester-long project and chatting casually with colleagues is actually genuinely useful.

It happens in my field (computer science) mostly because employers tell the departments that they want recruits with more "teamwork experience". Schools are too stupid to know that that's code for "We don't know what we want, so we'll ask for a management buzzword"

In contrast to the idiotic group projects, "update your coworkers constantly and bounce ideas off of them" is how work ACTUALLY gets done. I've only been in industry for a few years at this point, but what I've seen so far has only reinforced by distaste for group projects in school.

I've always considered estimates of how big the universe is or how much mass is in it to be akin to a dust mite trying to estimate the size of the Earth's oceans or the amount of water in it from behind a grain of sand buried two feet deep on a beach.

True enough; in fact, the relative sizes of the observable universe and ourselves are farther apart than the examples you used.

But (and I'm speaking as an astrophysicist), it's quite feasible for us to do this, thanks to observation and mathematics. One of the long-running problems (I don't mean "impossible things to do," but "tasks to solve") in astrophysics has been how to measure distance in space, where we can't just run out a tape measure between objects.

The technique to use depends on the kind of size scale you're dealing with. Distances within the solar system can be measured from parallax very accurately. In fact, the ancient Greeks even had good estimates of the size of the Earth and Moon and their distance. We've known the distances between the planets since the 1700s, using parallax during the "transits" of Venus across the Sun. And we can even use the Earth's motion around the Sun (now that we have that measured) to get us the distances to the stars in our neighborhood in the Milky Way.

To get the distances to nearby galaxies, we can look for stars of types with known luminosity (Wattage) in those galaxies, compare with how bright they appear to us, far from them, and quickly get their distances, knowing how light fades with distance. I just had a classful of astronomy students do this as a lab project.

For more distant galaxies, you might use Hubble's Law of the expansion of the Universe, which lets you take a galaxy's motion (easily measured from its chemical spectrum, through redshift) and solve for distance. As long as you know the universe's expansion rate ("Hubble's Constant"), it's simple.

We didn't know Hubble's constant with much accuracy until about a decade ago, but several different experiments have let us solve for it with pretty high precision. It also gets us the age of the universe, which is ~13.7 billion years.

Since light travels 1 light year in a year, then the farthest we can see—the size of the observable universe—is 13.7 billion light years away.

It took science a lot of time and work to get to this point, but squeezing down the uncertainties in each rung of the "distance ladder," we've been able to get measurements of the size of the observable universe with known precision.

One good thing about group projects in college is that it gives you something to talk about in interviews when you are asked about things like 1. experience working in teams, 2. overcoming adversity, 3. interpersonal skills...etc..

If the recent tachyon quandary ends up as true, that pretty much shoots all of that to hell, though, doesn't it?

On another astronomical note, I checked the blogs linked to your profile, but didn't see an email for you. Can you send me a contact link to ravenloff@hotmail.com? I've got some very specific questions I've been doing some research on Sol-type stars lately without much to show for it.

Long decades ago I was in on an early attempt at group projecting. The sociology instructor gave a question and formed us into groups, telling us to attempt an answer after the weekend. I gave the answer. He said that indeed that was the answer, but what mattered was actually not the answer, but the reasoning. I gave the reasoning. He said that was the reasoning, revoked the assignment, and deconvened the groups.

My pardonable smugness about this was to receive a quick rebuke. The next group assignment was crafted to have no right answer - the right answer was the consensus the group achieved. In fact you were in trouble for obstruction if you tried to find and impose a right answer. So, that showed me.

We're involved in a society-wide experiment to explore the limits of competence. Shall we just hire the blind pilot? It would be non-discriminatory, and very good for his self-esteem, but we maintain a stubborn belief that sighted pilots are necessary. Shall we just hire the bitchy jerk for the department of motor vehicles? Competence there is not very necessary (though it is regretfully valued when not present). What I'm finding - though "we" don't seem to be finding it yet as a society - is that the right answers have a damnable habit of trumping consensus. And they show up belatedly in areas of society where many wish they would not.

@ScottM:If the recent tachyon quandary ends up as true, that pretty much shoots all of that to hell, though, doesn't it?

No. I think of scientific knowledge as being like a web. Even if parts of it are missing, incomplete, or damaged other parts continue to function. Much of what we know, we will still know even if the neutrino thing turns out to be true.

The problem will not be in explaining how neutrinos go faster than light. The problem will be explaining why, if neutrinos go faster than light, why do so many things from relativity that are now proven "wrong" still appearing to be right?

Relativity and quantum mechanics both had the same problem with respect to classical physics. But it was shown that classical physics is what you get when you look at relativity at low speeds, or when you look at quantum mechanics with many billions of atoms.

Whatever new theory coems out of the neutrino measurement--and I highly doubt any such thing will happen--will still agree with the vast majority of what we know. Because what we know can't have been too far wrong, it has been very successful.

Whatever new theory coems out of the neutrino measurement--and I highly doubt any such thing will happen--will still agree with the vast majority of what we know.

Correct, and I'm with you on that. But, as to the age issue or the size of the universe, if the new theory (just spitballing...I don't expect Einstein to be upended) shows that such particles ARE traveling faster than the speed of light, even by just a smidge, over that length of time that would seem to suggest a significant difference in the expected width.

over that length of time that would seem to suggest a significant difference in the expected width.

Well, true, but we already have that, with inflationary cosmologies and whatnot.

The fact that we don't know the answer exactly doesn't meant that we can't have a pretty good idea of what the final must be. Like I said, you can ballpark it from a few numbers. If you want to get within a factor of 2 of whatever the right answer is you have to know a lot more than that.

But you can put lower and upper bounds on it. The universe has to be older than the age of the Earth, for example. The age of the Earth estimate doesn't depend on the speed of light at all.

It's hard to puzzle through a problem if someone doesn't have enough training or experience to know what methods might apply, or what has worked in the past.

Also, what everyone is saying about the problem with group projects is especially relevant to my field of study. Church is basically a long term group project. The teacher is pretty sharp, so I trust he knows what he is doing, but still...

"Of course everyone has to master concepts, but you can't reinvent the wheel every time you need to do some algebra"

Something that's been hinted at here, but not stated strongly enough IMO, is that it's pretty hard to teach concepts when you don't have some grasp of the basic facts that the concepts are trying to, ahhh, conceptualize. Would you agree with this as a general rule?

"Another reason for group work is that professors often times find it hard to know what misunderstanding a student has. "

No kidding. Last year my wife, after 16 years in the classroom, taught high school math online. The basic electronic-whiteboard application that the school used included a feedback feature (kind of like a classroom clicker, I think.) She said it was eye-opening (in a discouraging sort of way) to get to a point in the lecture, say "If you think the answer is X, check the green checkmark, if you think it's Y check the red X" and see how few kids were actually getting it. High school kids (and it sounds like your college students too) have an amazing poker-face ability, and are not going to admit they are dumb in front of you--OR their classmates--by saying they aren't getting it.

I despise group projects anywhere, but especially in school. They seem designed to make sure the largest number of students get the grade of the best member of their group. Maybe we should just give everyone an A because someone in the class got one.

I don't understand the dislike of rote learning. Not everything lends itself to it, but for the things that do it's marvelous. When was the last time you forgot your ABCs?

One good thing about group projects in college is that it gives you something to talk about in interviews when you are asked about things like 1. experience working in teams, 2. overcoming adversity, 3. interpersonal skills...etc..

-------------------

Actually, this point you make is not at all trivial. In coming up with new project ideas every semester, I used to think about how strong a bullet that work will be on a student's resume; how substantial will it be when they talk about it in an interview. I would stress that point in the first couple of classes and encourage them to make the most of that opportunity. They now had an incentive to do more than necessary if they wanted to and most students did.

About interpersonal skills and group dynamics, same thing -- one student who particularly resented a smart female groupmate listened to my advice and modified his attitude and theirs was the best project -- I practically told him that when he graduates after that semester and finds himself in a work environment he does not get to choose who he works with -- so better get used to working with everybody now.

In coming up with new project ideas every semester, I used to think about how strong a bullet that work will be on a student's resume; how substantial will it be when they talk about it in an interview.

I had an interesting online discussion about whether to bring up the fact that one plays "World of Warcraft" in an interview or on a resume. One person said, "I sure do! It's on there as 'Volunteer activities -- mentoring mentally retarded children.'" I could describe my group projects much the same way ...

My biggest aggravation was a group project in law school. I had a GPA in the bottom of the class (I'm not good at bullshitting). My group members, who statistically had to have had higher GPAs, were writing at maybe an eighth grade level. Poor diction, no understanding of the econ side of a law and econ class, aimless paragraphs, and missing thesis statements littered their parts of our group paper. I never minded having some of the lowest grades in the class until I could see the tripe that was somehow getting marked up higher. (Related note: even though I actually played WoW in class on occaision, I still contributed the most to the classroom discussion and received the highest grade in the class.)

The only group project I felt that had any real value was a Managment Game class I took in college. Basically, we ran a company (albeit a simplified one) and each one of the team was responsible for one part of the business, so if anyone was slacking, it was clearly evident to the rest of the team and the prof. I was in charge of marketing.

I think I should point out that I don't give group projects. I have groups do assignments in class. Which are normally not graded. And because the groups are grouped by ability no one gets to coast. If they don't work, nothing happens. They don't get to leave until it's done.

The groups are pretty quick to catch on what level they are in the class and that that's why they were grouped together. I don't imagine it helps people's self esteem, but I'm here to teach physics.

Basically, we ran a company (albeit a simplified one) and each one of the team was responsible for one part of the business

That actually does sound fun. The most fun I had on a group project was one where we negotiated a union contract. Two people were management and two people were union and you got points based on what you negotiated for your side.

She said it was eye-opening (in a discouraging sort of way) to get to a point in the lecture, say "If you think the answer is X, check the green checkmark, if you think it's Y check the red X" and see how few kids were actually getting it.

Physics education research has shown that students have literally medieval conceptions of physics, for example they belive in impetus (a force that moving objects carry with them that keeps them moving). I have no idea where they are getting these ideas from. I can only conclude some monk from the 14th century was nailed into a barrel and is periodically released to teach high school physics.

So nobody likes group projects, ergo group projects are baaaaaad. We want better educations, but we don't want to be uncomfortable.

If someone just wants to go off by themselves and work in a corner all day long, then I don't want them working with, above, or for me. These people ultimately wind up doing what they want to do, what they are comfortable with, and not what needs to be done. And they don't want to participate in the discussion about what needs to be done because they can't handle someone questioning them or asking them to support their reasoning.

...far better to let children puzzle through a concept than to drill it into their heads.

People who make such statements, do they remember their own childhoods? Puzzle through a concept with what? how? But even without that objection there's the fact that childhood is that time in our development when our heads are like sponges thirsting to be filled with facts facts facts. Concepts can coalesce around those facts later. In fact there can't be any concepts, not sustainable concepts, without facts to flesh them out.

The most successful industrial designer in the world is Jonathan Ive and he works alone.

Alex, does he have a workshop in the Himalayas or something? Last I checked he worked at the Apple HQ in Cupertino. He works with people every damn day. In the Jobs bio it's stated that Jobs visited with Ives in the physical mockup/prototype area every day.

He has tremendous say over the final designs, but he used to have to run everything by Jobs, and I suspect he still has to run everything by Cook.

THANK YOU for this website! My 6th grader has a semester math test coming up and his teacher is lousy at explaining things. This will lighten the load a lot as we try to review an entire semester of pre-algebra in 2 weeks. Between this and some Saxon Math exercises, I see an "A" in someone's future...

And on group projects: I agree with everyone else who says it's 1 or 2 people doing the work and everyone else coasting. The best one I've seen is my 6th grader's History class. They spend 95% of their time during the year playing a game called Historia, 4 kids to a team. But their grade is based on quizzes, and they get just a participation grade for Historia at the end of the year. For the latter, the teacher is watching this game unfold all year, and he's not stupid: he knows who is running things and who is blowing it off. From what I've seen so far, I expect the final participation grades will reflect that.

Some of us, even as children, resented the notion that we had to figure out what someone else had already figured out, when we could just learn what was known and go on to what was interesting.

In some sense, yes, it's better (for some value of better) to understand how things work, but it's inefficient to ask kids to invent from scratch some way of moving objects too heavy to lift. Someone already invented the wheel and it probably took them a great deal of time and effort to do so. It's inefficient to ask them to discover base 10 number systems, even if it is useful to understand that number systems can be counted with any other base system we decided to use. It's inefficient to duplicate those steps in human understanding. Worse, not everyone *can* as a child, duplicate those developments made by brilliant adults in History.

Mostly, though, it's inefficient. It takes a great deal of time and effort that is necessarily stolen from some other endeavor.

I'm way late to this thread, and it's great, but I have a couple points.

First, I used to teach standardized test courses, and still take on the occasional charity case. When you are teaching, say, SAT geometry, you have to just instill the basic rules. So, for example, you say the basic important things about what I call 45-45-90 triangles. It's just memorization, and rote application.

Something interesting happens after you teach it a few times and do a few problems over and over, though: you start to notice some really cool shit. You start to see why all the things are true, and much more.

The upshot here is that, in my own experience, the best way to learn something is often conclusion first, reasoning second.

Secondly, one of the very best pieces of advice that we've probably all gotten goes like: find out what successful people are doing and do those things and you will get their results. It's great advice. But think it through. Rationale for doing those things is completely secondary. There's a lot anyone can get out of mimicry regardless of understanding. And people who do mimic and who are smart will soon come to understand.

Joe, we already talked about ways in which group projects at work are different than group projects at school.

But we didn't talk much about how they're alike. And the differences highlighted were mainly that school projects sucked, I didn't learn anything, and one person (usually me) did all of the work. Work projects also suck but hopefully I get stuck on an A-team and hopefully my boss recognizes my contributions.

There are a whole raft of group dynamics to be plumbed and harnessed there. Teams that really function at a high level regularly engage in critical thinking and conflict. I think oftentimes in school and work we think a team is effective when they can quickly come to consensus and agree on something. They seem to be working together. But in reality, they haven't give one moment to questioning why their original idea might not be the best one, and no one in the group wants to raise objections as the group dynamic encourages belonging and singlemindedness. I think we shortchange kids by not teaching them to be critical thinkers, and we definitely discourage, whether passively or overtly, the initiation of conflict.

I feel like a crank lately so I'll stop ranting now. This thread is likely dead now anyway. Cheerio!

IMHO, when a teacher gives a group project, they are either trying to skate for while, or they are trying to "share the wealth"

I've assigned group projects and NOT for either of those reasons. One, I did it to mix things up. Lecturing/presenting gets stale after awhile. Also, Kirk Parker (or at least his wife) touched on another good reason to do it. Getting kids to talk in class is like pulling teeth. And getting them to talk is a good way to gauge if they are picking up what you're putting down. Similar to Kirk Parker's wife, I was initially surprised at how little my presentations were comprehended or retained. So getting them to talk gives me insight into how good of a job I am doing communicating my ideas to them.

I think oftentimes in school and work we think a team is effective when they can quickly come to consensus and agree on something.

That's not how I think about, or what what I think is, an effective team. And the failure of what you, Joe Schmoe, just described as the too-often, gone-to scheme of teamed-ness (all that quick consensus, and shit) strikes me as the very point of what most anti- "teaming as a value in and of itself, outcomes be damned" folks here have been posting.

I think oftentimes in school and work we think a team is effective when they can quickly come to consensus and agree on something.

Sometimes that can be success, if what is agreed on is a reasonable plan of action. I have been on many a group that had the opposite problem, people who wanted to talk, talk, talk instead of getting something done. The best groups talk (or research) as much as they need to to get moving and then they get to work already!

I am just getting a chance to check out the Khan site and it is really neat! I am thinking about brushing up on my stat skills and maybe doing the math problems at some point just for fun. I watched several of the history videos and one on black holes (which I enjoyed more than the history-probably because I know more history).

I can name a whole number of ways in which they're alike. To name them specifically mostly wouldn't be polite. Nor would it be either effective or efficient. In short, it would be a waste of time, and well do I know it. How about you talk about the ways in which they're alike, instead?

Group projects at work include specialization, specific responsibility, and hierarchy.

In my experience, this was true enough, sometimes. Other times, too often, not so much.

Because of this, they function well.

Sometimes they do, sometimes they don't. With all due respect, Freeman, and I mean that sincerely, how many years, and stretched even sketchily over how many decades, did you work in corporate environments (of whatever types)?

Scott: yup, pretty much. The 6th grade History teachers in our district have been tasked with teaching "World Cultures" - basically everything about history for the entire length of it (yes, that's a horrible idea, I know). This one teacher thought that being assigned such a task and trying to complete it by stuffing dates into 11-12 year old heads was stupid, so he came up with this game instead. It seems to give the kids a working knowledge of what makes up a civilization, how they interact with one another, what is a risk and what is an asset, and also familiarizes them with a whole list of cultures throughout history that many of them have never heard of before (the exception being my history-addled son, who is right now 2/3 of the way through The Last Days of Pompeii and thinks it's "fantastic"). I never thought I'd approve of letting my child learn a middle school core subject by playing a game, but I do - at least in this 1 instance.

I think we shortchange kids by not teaching them to be critical thinkers, and we definitely discourage, whether passively or overtly, the initiation of conflict.So much for the vaunted "socialization" that group projects allegedly bring. Cue Crack for feminization complaint.

Other than science labs, the only group projects I remember in school occurred when my 7th grade teacher wanted to watch the Watergate hearings during class.

College chem labs were all individual, but I remember working with, or rather, for, a deer-in-headlights freshman in general physics. IIRC, his father was a professor at Duke.

Years ago I learned that when interviewing straight-out-of-college software engineers that you needed to dig deep when they claimed they knew a subject because they did a group project in college (as an undergraduate).

"Yes, I wrote a compiler."

Tell me about it.

"It was a group, there were five of us, and we wrote a compiler."

What part did you do?

"We wrote a lexer, a parser, and a code generator."

Yes, but what part did you do?

"Well, I worked on the compiler."

Yes, but what did you actually code up?

"You know, there was a lexer, a parser, and ..."

No, I mean, exactly what part did you yourself write?

... Another few questions like this and I inevitably discovered that the candidate didn't do anything on the project at all!

After a couple of years of that I just gave up that line of questioning.

That is why, when interviewing for programming jobs, you always get asked to write some code on the whiteboard.

Are you troubled because Freeman didn't put enough qualifiers in there?

No. I am not troubled by that (nor was I thinking in the way you evidently are). You've missed the point of my comment. Also, I'm 100% sure that Freeman is capable of ... well, pretty much everything. Which, among other things, means she doesn't need the likes of you to address what the likes of me has to say.

I too teach physics and I believe the reason most people believe in impetus is that on earth IT WORKS. On earth everything stops eventually unless you do something to keep it moving.

I tell my classes that they are right to think that on earth everything stops eventually--but then I go on to bring up some problems with the impetus idea (why would a soccer ball stop quicker on tall grass than on asphalt?) and tell them that there is a different way of looking at things that turns out to work better. We then go on to Newton's first two laws of motion.

Metaphorically, impetus is Kahneman's System 1 and Newton is System 2. People who go on in physics get so used to Newton that it becomes part of System 1.

This one teacher thought that being assigned such a task and trying to complete it by stuffing dates into 11-12 year old heads was stupid, so he came up with this game instead. It seems to give the kids a working knowledge of what makes up a civilization, how they interact with one another, what is a risk and what is an asset, and also familiarizes them with a whole list of cultures throughout history that many of them have never heard of before

Sounds a lot like an academically watered-down version of Sid Meier's Civilization. Honestly, though, that game is immensely educational, but you have to read up on the Civilopedia on various things...they don't spoon-feed it to you like I assume the 6th grade game does.

I tell my classes that they are right to think that on earth everything stops eventually--but then I go on to bring up some problems with the impetus idea (why would a soccer ball stop quicker on tall grass than on asphalt?) and tell them that there is a different way of looking at things that turns out to work better.

I showed them 4 situations:

Pushing a book across a tableRolling a ball across a tableThrowing a ballThe motion of planets

If you believe in impetus you need 4 sets of of laws of motion for these cases. If you use Newton's laws, you just need one.

And they can repeat this back to me, but when you give them an unfamiliar problem they almost always retreat to impetus.

They have a hard time distinguishing force from velocity and acceleration; to them those are all more or less the same. And of course to them "moving" and "not moving" are a hard and fast distinction. Things that are "not moving" are forever and always not moving, and so they have a very hard time processing that a ball thrown up stops moving at the peak of its motion.

And the Third Law? Black magic. They don't believe in it even though they may repeat it to you on exams. You can show this by changing the context of the problem.

Also, they think that if you know the acceleration you know what the value of one force on an object is. And it's like pulling teeth to get them to make free body diagrams.

And have you noticed they can solve problems without grasping elementary concepts and vice versa? I knew that was true, but I had demonstrate the lack of correlation with the data from my own class before I really felt it.

It wouldn't be so hard if I wasn't trying to reach 50% of the class. You can split them up into roughly equal groups:

the bright and hardworkingthe bright and lazythe slow and hardworkingthe slow and lazy

Group 1 will do well whatever you do, and Group 4 will do badly whatever you do. It's 2 and 3 that take all the work. I've got my students in 2 engaged enough to do their work, but I'm not doing much for group 3 I'm afraid. And my efforts are boring group 1.

The thread lives. Rcommal and Freeman (and David-2), lots of great stuff that I'd like to respond to if I get a chance today. I've got a big meeting at 1 that I should be prepping for all morning, so I'll try to resist the siren song of Althouse comments. Might have to wait for another similar thread.

chrisgadsen, if you read Ann's original post, you'll see she includes an adder about Khan Academy creating enough free time for group projects. I didn't take the bait, went off-script and tried to defend group projects, but admittedly haven't done so very well yet. I'm not trying to proseltyze; just explain what I think. I think there's a lot of merit in group projects, and almost none of it is to impart a specific skill or lesson that would normally be imparted through lectures or textbooks.

Group projects at work include specialization, specific responsibility, and hierarchy. Because of this, they function well.

Freeman, you have shown yourself to be an intelligent, articulate person with whom I agree on many issues. Now that we've gotten to know each other, do you mind if I say to you that this is utter bullshit? It's true maybe 25% of the time, if you're lucky.

Group projects are useful in academic settings for change of pace, giving the instructor insight into comprehension/retention of course matter, and giving the students a chance to experience group dynamics.

Hypothesis: Groups can be good. Not all bad. Is this blog better off because of its variety of commenters? Have we loosely organized and created something bigger than Ann's blog itself? Individuals are the wellsprings of ideas; groups are needed to realize those ideas on large scales. So let's say groups in general are good and necessary. As such, why would we deny children the opportunity to learn about something so valuable?

In a previous post we all decried Newt and Obama as textbook-smart and not necessarily street-smart. But now that we're talking about group projects many of you retreat into textbook-smart approaches. There's comfort between the covers, apparently. Group dynamics are a great chance to experience and practice their street-smarts. I don't espouse a single method for dealing with groups, but there are endless tips and opportunities for students to expand their awareness of themselves and their classmates.

Biggest reason for failure in classrooms is incorrect baseline for success. If you want them to learn a skill and cross-pollinate it among themselves, it will fail. The baseline for success should be on the group interaction, not the output.

If you follow my criteria for success, then all of you who did entire projects on your own failed miserably. You accepted a leadership role and proceeded to lead a listless ship. If you had somehow engaged your teammates, you may have had a lesser output, or you might have been surprised at what your teammates brought to the table. Engaging everyone is really hard and not always doable, but if you want to be a leader then step up to the plate.

I apologize if this sounds like an 'eat your peas' approach. Please just think about it and let me know what you think.

My credentials: I have worked at high-tech Fortune 1000 companies for almost 20 years and have also taught college classes on the side. My ability to navigate working groups and create tangible results is what led to my being tapped for management positions. While no means extensive, my thoughts are informed both by research and practical experience. Moreso by experience, and I've been infinitely more informed by my failures than my successes.

ah shite; google/blogger wiped out a long post of mine where I explained what I value in group projects. Short synopsis: groups can be good (look at these blog comments), using groups to impart a skill through cross-pollination is ineffective--the focus is on the group interaction, not the output; groups can enable kids to practice and experience street-smarts rather than book-smarts, companies are NOT the model of effective group work, and I think groups do have their place in education, just not as typically implemented.

What, you can't differentiate instruction? Yeah, neither can I. At least, not enough to reach all four groups.

I no longer do the third law when I do the first two. Instead, my sequence is now:forces and first two lawsimpulsemomentum defined as accumulated force (what happens to a force when it stops being exerted on an object; does it disappear? No, it has turned into momentum.)impulse-momentum theoremconservation of momentumthird law as a consequence of conservation of momentum

I do silly demonstrations like trying to walk when there is no friction between my shoes and the floor, and ask questions like how come my foot pushes backwards when I walk but I go forward. But, yeah, they have real trouble "getting it."

The last two years, I've done static equilibrium before Newton's laws, and had them learn free-body diagrams in that situation. It seems to help.

Phil Mazur tells the story of giving his Harvard introductory physics students two problems. One shows a circuit diagram and asks what happens to current, resistance, etc, when a particular switch is closed. The second shows the same diagram with numbers and asks them to calculate current, resistance, etc. He thought just about everyone would get the first and maybe 70% would get the second. I.e., the understanding was easy and running the numbers was harder. Seventy percent did get the second but less than half got the first. They had learned to plug in formulas but didn't really understand what was going on.

My wife uses the Khan project to relearn some math that she hasn't seen for many years. She likes it, but says there aren't proper exercises available for all the lessons, and they're not conveniently linked to the lessons.

Some schools find that ditching discovery based learning for traditional methods results in great improvement.

Didn't say group methods were superior to traditional methods. Just advocated that group learning was not as useless as everyone else seems to think.

Also in a previous post we decried Obama and Newt for their book smarts and lack of street smarts. Now we're advocating a full embrace of book smarts again?

Group exercises help students gauge their own abilities against those of their teammates. It's a useful feedback loop for them. Something Newt and Barry could've used a little more of, apparently. It also takes street smarts to have a constructive impact on a group. Kids who aren't good at it should strive to be. They'll be effective people.

And if you experienced 100% success in all your work projects, you never had to change course or water down your final product due to insufficient preparation, and your success baseline was perfectly tied to your company's goals, then I commend you. You're the first. This company must monopolize its market. Otherwise you're deluding yourself that everything was perfect.

Also in a previous post we decried Obama and Newt for their book smarts and lack of street smarts. Now we're advocating a full embrace of book smarts again?

You know what fixes a lack of street smarts? Dodge ball or old-school bombardment. An hour a day. And not with the wussie red, textured rubber balls either. Nerf footballs wrapped liberally in athletic tape.